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calculus-tutor skill

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This skill helps you master single and multivariable calculus with rigorous proofs and practical applications across limits, derivatives, integrals, sequences,

npx playbooks add skill sandraschi/advanced-memory-mcp --skill calculus-tutor

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SKILL.md

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---
name: calculus-tutor-single-multivariable
description: Comprehensive calculus expert covering limits, derivatives, integrals, sequences, series, and multivariable calculus with rigorous proofs and practical applications
license: Proprietary
---

# Calculus Tutor (Single & Multivariable)
> **Status**: ⚠️ Legacy template awaiting research upgrade
> **Last validated**: 2025-11-08
> **Confidence**: 🔴 Low — Legacy template awaiting research upgrade

## How to use this skill
1. Start with [modules/research-checklist.md](modules/research-checklist.md) and capture up-to-date sources.
2. Review [modules/known-gaps.md](modules/known-gaps.md) and resolve outstanding items.
3. Load topic-specific modules from [_toc.md](_toc.md) only after verification.
4. Update metadata when confidence improves.

## Module overview
- [Core guidance](modules/core-guidance.md) — legacy instructions preserved for review
- [Known gaps](modules/known-gaps.md) — validation tasks and open questions
- [Research checklist](modules/research-checklist.md) — mandatory workflow for freshness

## Research status
- Fresh web research pending (conversion captured on 2025-11-08).
- Document all new sources inside `the Source Log` and the research checklist.
- Do not rely on this skill until confidence is upgraded to `medium` or `high`.

Overview

This skill is a comprehensive calculus tutor covering single-variable and multivariable topics: limits, derivatives, integrals, sequences, series, and multivariable calculus. It provides rigorous proofs, step-by-step worked problems, and practical application guidance, but currently exists as a legacy template that requires a research refresh before full reliance. Use it for structured learning, preparing proofs, or constructing course-ready explanations once confidence is upgraded.

How this skill works

The skill organizes topics into modular sections that present definitions, theorem statements, proofs, example problems, and application notes. For each topic it aims to offer formal proofs, computational techniques, and heuristic intuition, plus problem templates learners can adapt. Note: content requires verification and source updates to reach medium/high confidence before use in assessment or publication.

When to use it

When you need a rigorous walkthrough of a calculus proof or theorem
When preparing lecture notes or problem sets for single- and multivariable calculus
When learning techniques for limits, differentiation, integration, or series convergence
When designing applied math examples that use gradients, divergence, curl, or multiple integrals
When you want structured step-by-step solutions for homework or exam practice

Best practices

Verify each proof and example against up-to-date references before using in teaching or publication
Start with foundational single-variable modules before progressing to multivariable topics
Cross-check computational results numerically when possible to catch algebraic errors
Annotate examples with application contexts (physics, engineering, data science) to enhance transfer
Document new or updated sources and mark refreshed modules with an increased confidence level

Example use cases

Derive and explain the chain rule, product rule, and rigorous epsilon-delta limit proofs for a calculus course
Work through convergence tests for series with stepwise logic and comparison examples
Compute and interpret gradients, directional derivatives, and tangent planes in multivariable problems
Set up and evaluate double and triple integrals for volume, mass, and center-of-mass applications
Generate problem sets with full solutions for midterm or final exam preparation

FAQ

Is the content ready for direct classroom use?

Not yet—this is a legacy template that needs a research refresh and source verification before use in formal instruction.

Will the skill provide step-by-step proofs and computations?

Yes—the design emphasizes rigorous proofs and worked computations, but confirm each item during the refresh process.